Explicit reconstruction of the entanglement wedge

Abstract

AdS/CFT is a duality between the gravitational theory on asymptotically AdS space and the conformal theory defined on its boundary. Although many nontrivial checks were made and much is known about the dictionary that interpolates both side of the duality, compilation of the dictionary is still far from being complete. One of the major issues that needs more elucidation is the problem of subregion duality

what information of the bulk a given boundary subregion encodes. Although the proof given by Dong, Harlow, and Wall states that the entanglement wedge of the bulk should be encoded in boundary subregions, explicit procedure for reconstructing the entanglement wedge remained a mystery for some time. Based on [1], a generalisation of the mode sum approach to smearing functions that incorporates reconstruction on the entanglement wedge is described. Contrary to naive expectations, there is no need to solve the wave equation on a complicated coordinate patch. This hard problem is transferred to a less hard but tractable problem of matrix inversion.